Semiclassical structure of Hamiltonians

The structure of few-body Hamiltonian matrices is studied in the semiclassical regime. Given (A^₁(q^,p^),A^₂ (q^,p^)), a pair of operators, it can be shown that, under quite general conditions, A^₂ takes the form of a banded matrix in the ordered eigenrepresentation of A^₁. Moreover, the bandwidth depends only on {} and certain generalized microcanonical averages. In particular, if H=H₀+{ε}V, this implies that the perturbed Hamiltonian is banded in the appropriately ordered unperturbed basis.